Problem: Rewrite as a simplified fraction. ${1.\overline{29} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 129.2929...\\ 1x &= 1.2929...\end{align*}}$ Subtracting the two equations, we have: ${99x = 128}$ ${x = \dfrac{128}{99}} \text{or} {1 \dfrac{29}{99}}$